A woman embraces her boyfriend, a new recruit of the Ukrainian army heading toward eastern regions.

Photo: Sergei Supinsky, AFP/Getty Images

A woman embraces her boyfriend, a new recruit of the Ukrainian army...

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TOPSHOTS A priest blesses new volunteer recruits of the Ukrainian army 'Donbass' battalion during a military oath ceremony of the National Guard near the Novi Petrivtsi village not far from Kiev, on June 23, 2014. Some 600 new volunteer recruits of the battalion, mainly representatives of the eastern Donbass region of Ukraine, who followed combat training during three weeks will take part in the military operation against armed pro-Russian militants in the east of the country. Ukraine pressed German Chancellor Angela Merkel and other Western allies today to help end a pro-Russian uprising that has continued to rage in the industrial east despite Kiev's unilateral ceasefire. AFP PHOTO / SERGEI SUPINSKYSERGEI SUPINSKY/AFP/Getty Images

Donetsk, Ukraine -- Pro-Russian insurgents in eastern Ukraine agreed Monday to respect a cease-fire declared by the Ukrainian president, raising hopes for an end to months of fighting that have killed hundreds and ravaged the country's industrial heartland.

The announcement came as the Russian and U.S. presidents traded demands over the conflict. Russian President Vladimir Putin urged direct talks between the government and the rebels, as President Obama warned Putin that Moscow will face additional sanctions if it does not help ease the crisis.

The insurgents' pledge to respect the cease-fire came on the first day of talks between a former Ukrainian president, the Russian ambassador, European officials and the eastern separatists who have declared independence. While the government side was nominally not represented, ex-President Leonid Kuchma attended the discussions at the request of the sitting president.

The negotiations were launched in line with President Petro Poroshenko's peace plan, which started Friday with a weeklong unilateral cease-fire in the fighting that has killed more than 350 people and forced tens of thousands to flee their homes.

The insurgents had previously demanded the Ukrainian military withdraw its troops from the east as a condition for any talks, so the pledge represented a softened stance that raised expectations that the cease-fire could hold.

Since the cease-fire was declared Friday, the Ukrainian government has accused the rebels of firing at government positions, while insurgents blamed Ukrainian forces for failing to honor the promise to halt hostilities. Poroshenko has said government troops will fire back if attacked.

In Moscow, the Kremlin said Putin underlined in his conversation with Obama that to normalize the situation in eastern Ukraine, it's necessary to "effectively end fighting and start direct talks between the conflicting parties."

White House spokesman Josh Earnest said Obama urged Putin to use his personal influence with the separatists to promote peace and stability in Ukraine, stop backing the insurgents and halt the flow of arms across the border.